已知a,b属于(0,90度),且满足sinb/sina=cos(a+b),

题目

已知a,b属于(0,90度),且满足sinb/sina=cos(a+b),

答案

(1)证明：sinb=sin(a+b-a)=sin(a+b)cosa-sinacos(a+b)=sinacos(a+b)
so:sin(a+b)cosa=2sinacos(a+b)
tan(a+b)=2tana
(2)证明：sinb/sina=cosacosb-sinasinb两端同除以cosb
tanb/sina=cosa-sinatanb
tanb(1+sina^2)=cosasina
tanb=sinacosa/(1+sina^2)
(3)由(1)
(tana+tanb)/(1-tanatanb)=2tana
so:tanb=tana/(1+2tana^2)